By what factor will the $r.m.s.$ velocity change if the temperature is raised from $27^\circ C$ to $327^\circ C$?

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the root mean square velocity of its molecules at $100 \ K$,what is the new root mean square velocity?

At a temperature of $27 \, ^\circ C$,the $rms$ speed of a gas is $1930 \, m/s$. The gas is:

Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

At temperature $T$,$N$ molecules of gas $A$ each having mass $m$ and at the same temperature $2N$ molecules of gas $B$ each having mass $2m$ are filled in a container. The mean square velocity of molecules of gas $B$ is $v^2$ and the mean square of the $x$-component of velocity of molecules of gas $A$ is $w^2$. The ratio of $w^2/v^2$ is:

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$: